The convection equations relating the Nusselt, Reynolds, and Prandtl numbers can be rearranged to show that for gases, the heat-transfer coefficient h_c depends on the absolute temperature T and the group √U_∞/x. This formulation is of the form h_c,x = CTⁿ √U_∞/x , where n and C are constants. Indicate clearly how such a relationship could be obtained for the laminar flow case from Nu_x = 0.332 Re_x ^0.5 Pr^0.333 for the condition 0.5 < Pr < 5.0. State restrictions on method if necessary.

GIVEN

• For laminar flow: Nu_x = 0.332 Re_x ^0.5 Pr^0.333 for 0.5 < Pr < 5.0

ASSUMPTIONS

• Gas behaves as an ideal gas